Reals n-generic relative to some perfect tree

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Reals n-generic relative to some perfect tree

We say that a real X is n-generic relative to a perfect tree T if X is a path through T and for all Σn(T ) sets S, there exists a number k such that either X|k ∈ S or for all σ ∈ T extending X|k we have σ / ∈ S. A real X is n-generic relative to some perfect tree if there exists such a T . We first show that for every number n all but countably many reals are n-generic relative to some perfect ...

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ژورنال

عنوان ژورنال: Journal of Symbolic Logic

سال: 2008

ISSN: 0022-4812,1943-5886

DOI: 10.2178/jsl/1208359051